Transmission parameter, i.e. the potential number of new infections per infected individual at the next time step

\(\beta > 0\)

\(\gamma\)

Proportion of infectious population that remains infectious at next time step (which includes the removal of infections through passive detection)

\(0 < \gamma < 1\)

\(\varphi_{t}\)

Number of infections detected (and treated) at time t

\(\varphi_{t} > 0\)

\(\varepsilon_{t}\)

Escape probability: the proportion of infections that escape treatment at time t

\(0 < \varepsilon_{t} < 1\)

\(p\)

Proportion of population that is (patently) infected

\(0 < p < 1\)

\(\upiota\)

Number of index cases investigated per unit time

\(\upiota > 0\)

\(\upnu\)

Number of neighbours of passively-detected index cases investigated

\(0 < \nu < N\)

Fixed property of programme

\(\uptau\)

Targeting ratio: ratio of the size of a random sample that would be need to be tested and treated, to the number actually treated, in order to achieve the same number of effective treatments. This is a measure of clustering of malaria infections